The advent of dual modality PET/CT scanners has significantly enhanced the physician's armamentarium for the diagnosis and staging of cancer as well as for therapy planning and monitoring response to therapy. Our earlier work demonstrated that PET/CT scanners have synergies in the use of the x-ray CT image for anatomical localization of the PET functional information and attenuation correction of the PET emission data. PET/CT scanners are now in routine use for the diagnosis and staging of cancer. However, there are clinically relevant scenarios where improving the quantitative accuracy of PET/CT imaging is both important and challenging. An exciting development is the use of PET/CT imaging to accurately measure a tumor's characteristics both before and during therapy to determine as early as possible the efficacy of the treatment. The most significant challenges to quantitative accuracy come from respiratory motion, partial volume effects, and estimation of the attenuation coefficients for high atomic number materials such as bone, metal, and contrast agents. Specific abnormalities where combinations of these difficulties occur are in imaging lung cancer and bone metastases from breast cancer. We hypothesize that improved quantification can be achieved through the development of three approaches: (1) combining low-dose x-ray imaging with dual energy CT for PET attenuation correction, (2) the use of respiratory-correlated PET/CT with image registration, and (3) the use of PET scanner resolution and CT-derived boundary information in the PET image reconstruction or in post-reconstruction image processing. The improved quantification of tracer uptake will increase the accuracy of information used to guide therapeutic choices, directly benefiting patient care. Accurate PET/CT measurements of early response will be critical in determining the best cancer therapy option for each patient in a timely manner and in sparing patients the morbidity and cost of ineffective treatments.